Question

Construa num mesmo sistema e eixos os gráficos de:

a) f(x) = 2x e g(x) = log₂ˣ

b)f(x) = ($\frac{1}{2}$)ˣ e g(x) = log$\frac{1}{2}$ˣ

Answer 1

vamos lá...

a)

$y=2^x$

X  |  Y
-2 | 1/4  ⇒  2⁻²=(1/2)²=1/4  (-2,1/4)

-1 | 1/2 ⇒  2⁻¹=1/2   (-1,1/2)

0  |  1  ⇒  2⁰=1   (0,1)

1  |  2  ⇒ 2¹=2  (1,2)

2  | 4  ⇒ 2²=4  ( 2,4)


$g(x)=\log_2x$

$X~~~|~Y \\ 1/4~|-2\mapsto2^y=1/4\mapsto2^y=2^{-2}\mapsto y=-2~~~(1/4,-2) \\ \\ 1/2~|-1\mapsto2^y=1/2\mapsto2^y=2^{-1} \mapsto y=-1~~(1/2,-1) \\ \\ 1~~~|~~0 \mapsto2^y=1\mapsto2^y=2^0\mapstoy=0~~~(1,0) \\ \\ 2~~~|~~1\mapsto2^y=1\mapsto2^y=2^1\mapsto y=1~~~(2,1) \\ \\ 4~~~|~~2 \mapsto2^y=4\mapsto2^y=2^2\mapstoy=2~~~(4,2)$

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b)
$f(x)=( \frac{1}{2} )^x \\ \\ X~~~|~~Y \\ -2~|~4 \mapsto(1/2)^{-2}=2^2=4~~~~(-2,4) \\ \\ -1~|~2\mapsto(1/2)^{-1}=2^1=2 ~~~~(-1,2) \\ \\ 0~~~|~~1~\mapsto(1/2)^0=1~~~~(0,1) \\ \\ 1~~|~1/2~\mapsto(1/2)^1=1/2~~~(1,1/2) \\ \\ 2~~|~1/4~\mapsto(1/2)^2=1/4~~~(2,1/4)$ 

$g(x)=\log_{ \frac{1}{2} }x \\ \\ X~~|~Y \\ 4~~~|~-2~\mapsto(1/2)^y=4\mapsto2^{-y}=2^2\mapsto-y=2\mapsto y=-2~~(4,-2) \\ \\ 2~~|~-1~\mapsto(1/2)^y=2\mapsto2^{-y}=2^1\mapsto-y=1\mapsto y=-1~~~(2,-1) \\ \\ 1~~|~~0\mapsto(1/2)^y=1\mapsto2^{-y}=2^0\mapsto y=0~~~(1,0) \\ \\ 1/2~|~1~\mapsto(1/2)^y=(1/2)^1\mapsto y=1~~~(1/2,1) \\ \\ 1/4~~|~2~\mapsto(1/2)^y=1/4\mapsto(1/2)^y=(1/2)^2\mapsto y=2~~~~(1/4,2)$